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Basics
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4 Plot each of the points (2, 4), ( 6, 3), ( , 2 ), ( 5, 8), ( 2 , 3), (1/3, 19/4) on a pair of cartesian coordinate axes Label each point 5 Plot each of these planar loci on a separate set of axes (a) (b) (c) (d) (e) (f) {(x, y): y = 2x 2 3} {(x, y): x 2 + y 2 = 9} y = x3 + x x = y3 + y x = y2 y3 x2 + y4 = 3 {(x, y): x 2 + y 2 < 4} {(x, y): y > x 2 } {(x, y): y < x 3 } {(x, y): x 2y + 3} {(x, y): y x + 1} {(x, y): 2x + y 1} The line through the points ( 5, 6) and (2, 4) The line perpendicular to the line through (1, 2) and (3, 4) The line 2y + 3x = 6 x 4y The line =6 x+y The line through the points (1, 1) and ( 8, 9) The line x y = 4 The line parallel to 3x + 8y = 9 and passing through the point (4, 9) The line perpendicular to x + y = 2 and passing through the point ( 4, 8) The line passing through the point (4, 6) and having slope 8 The line passing through ( 6, 4) and (2, 3) The line passing through the origin and having slope 6 The line perpendicular to x = 3y 7 and passing through ( 4, 7)
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6 Plot each of these regions in the plane (a) (b) (c) (d) (e) (f)
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7 Calculate the slope of each of the following lines: (a) (b) (c) (d) (e) (f)
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8 Write the equation of each of the following lines (a) (b) (c) (d) (e) (f)
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9 Graph each of the lines in Exercise 8 on its own set of axes Label your graphs 10 Which of the following is a function and which is not Give a reason in each case
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CHAPTER 1 Basics
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(a) (b) (c) (d) (e) (f) (g) (h) (i) f assigns to each person his biological father g assigns to each man his dog h assigns to each real number its square root f assigns to each positive integer its cube g assigns to each car its driver h assigns to each toe its foot f assigns to each rational number the greatest integer that does not exceed it g assigns to each integer the next integer h assigns to each real number its square plus six f (x) = 3x 2 x x+2 g(x) = x h(x) = x 3 x 2 f (x) = 3x + 2 g(x) = 2x x2 h(x) = x + 3 sin(8 /3) tan( 5 /6) sec(7 /4) csc(13 /4) cot( 15 /4) cos( 3 /4)
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11 Graph each of these functions on a separate set of axes Label your graph (a) (b) (c) (d) (e) (f)
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12 Calculate each of the following trigonometric quantities (a) (b) (c) (d) (e) (f)
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13 Calculate the left and right sides of the twelve fundamental trigonometric identities for the values = /3 and = /6, thus con rming the identities for these particular values 14 Sketch the graphs of each of the following trigonometric functions (a) (b) (c) (d) (e) (f) f (x) = sin 2x g(x) = cos(x + /2) h(x) = tan( x + ) f (x) = cot(3x + ) g(x) = sin(x/3) h(x) = cos( + [x/2])
15 Convert each of the following angles from radian measure to degree measure
(a) (b) (c) (d) (e) (f) = /24 = /3 = 27 /12 = 9 /16 =3 = 5